Afterhyperpolarization potential modulated by local [K+]o in K+ diffusion-restricted extracellular space in the central clock of suprachiasmatic nucleus

Background Intercellular coupling is essential for the suprachiasmatic nucleus (SCN) to serve as a coherent central clock. Synaptic release of neurotransmitters and neuropeptides is critical for synchronizing SCN neurons. However, intercellular coupling via non-synaptic mechanisms has also been demonstrated. In particular, the abundant perikaryal appositions with morphological specializations in the narrow extracellular space (ECS) may hinder molecular diffusion to allow for ion accumulation or depletion. Methods The SCN neurons were recorded in the whole-cell current-clamp mode, with pipette filled with high (26 mM)-Na+ or low (6 mM)-Na+ solution. Results Cells recorded with high-Na+ pipette solution could fire spontaneous action potentials (AP) with peak AHP more negative than the calculated value of K+ equilibrium potential (EK) and with peak AP more positive than calculated ENa. Cells recorded with low-Na+ pipette solution could also have peak AHP more negative than calculated EK. In contrast, the resting membrane potential (RMP) was always less negative to calculated EK. The distribution and the averaged amplitude of peak AHP, peak AP, or RMP was similar between cells recorded with high-Na+ and low-Na+ solution pipette. In a number of cells, the peak AHP could increase from more positive to become more negative than calculated EK spontaneously or after treatments to hyperpolarize the RMP. TTX blocked the Na+ -dependent APs and tetraethylammonium (TEA), but not Ba2+ or Cd2+, markedly reduced the peak AHP. Perforated-patch cells could also but rarely fire APs with peak AHP more negative than calculated EK. Conclusion The result of peak AHP negative to calculated EK indicates that local [K+]o sensed by the TEA-sensitive AHP K+ channels must be lower than bulk [K+]o, most likely due to K+ clearance from K+ diffusion-restricted ECS by the Na+/K+-ATPase. The K+ diffusion-restricted ECS may allow for K+-mediated ionic interactions among neurons to regulate SCN excitability.

The suprachiasmatic nucleus (SCN) in the hypothalamus is the central clock that coordinates peripheral clocks to control circadian rhythms in mammals [1]. The SCN neurons exhibit a circadian rhythm in spontaneous firing rate both in intact animals [2] and in isolated hypothalamic slices [3e5]. The autonomous oscillation in the circadian clock arises from a transcriptional translational feedback loop leading to~24 h oscillation of clock genes and proteins within individual SCN neurons [6,7]. Indeed, most individual SCN neurons in dissociation still exhibit circadian variation in the spontaneous firing rate, albeit with various periods and phases [8e10]. The scattered periods and phases become narrower in SCN explants [8] and narrowest in the circadian period of locomotor activity [8,9]. Together, the results indicate that the SCN contains cell-autonomous circadian oscillators that are synchronized to act as a coherent oscillator.
Intercellular coupling of SCN neurons is critically dependent on chemical communication via the release of neurotransmitters and neuropeptides, particularly GABA and vasoactive intestinal peptide (for review, see Ref. [11]). However, non-synaptic communication must be present to account for the functional circadian clocks in the developing SCN before the occurrence of significant synaptic connections [12e14]. In the rat SCN, neuronal synchronization is known to occur in the absence of Ca 2þ -dependent synaptic transmission [15]. The SCN is tightly packed with small neurons and has abundant perikaryal appositions [16], which may favor non-synaptic communications such as electrotonic coupling via gap junctions [17e19] and ionic interactions (see Ref. [20]). In particular, the abundant perikaryal appositions with morphological specializations in the narrow extracellular space (ECS) could increase the tortuosity to effectively slow molecular diffusion, allowing ion accumulation or depletion to occur in the diffusionrestricted ECS.
In this study, we used patch-clamp recordings to investigate the spontaneous AP in neurons from reduced, acute rat SCN slices. We showed that the SCN neurons could fire spontaneous APs with large peak afterhyperpolarization potential (AHP) more negative than the calculated value of K þ equilibrium potential (E K ) in whole-cell and even in perforated-patch recordings. In contrast, the resting membrane potential (RMP) was always less negative than calculated E K . The result indicates that local [K þ ] o in the ECS sensed by the AHP K þ channels must be lower than bulk [K þ ] o , most likely due to K þ clearance from the K þ diffusion-restricted ECS by the Na þ /K þ -ATPase. The ability of local [K þ ] o to regulate peak AHP amplitude may allow for the K þ diffusion-restricted ECS to mediate ionic interactions among neurons to regulate SCN excitability.

Hypothalamic brain slices and reduced SCN preparations
All experiments were carried out according to procedures approved by the Institutional Animal Care and Use Committee of Chang Gung University (IACUC Approval No.: CGU109-110). SpragueeDawley rats (18e24 days old) were kept in a temperature-controlled room under a 12:12 light:dark cycle (light on 0700e1900 h). Lights-on was designated Zeitgeber time (ZT) 0. For daytime and nighttime recordings, the animal was killed at ZT 2 and ZT 10, respectively. Hypothalamic brain slices and reduced SCN preparations were made as described previously [21,22]. An animal of either sex was carefully restrained by hand to reduce stress and killed by decapitation using a small rodent guillotine without anaesthesia, and the brain was put in an ice-cold artificial cerebrospinal fluid (ACSF) prebubbled with 95% O 2 e5% CO 2 . The ACSF contained (in mM): 125 NaCl, 3.5 KCl, 2 CaCl 2 , 1.5 MgCl 2 , 26 NaHCO 3 , 1.2 NaH 2 PO 4 , 10 glucose. A coronal slice (200e300 mm) containing the SCN and the optic chiasm was cut with a DSK microslicer DTK-1000 (Ted Pella, Redding, CA, USA), and was then incubated at room temperature (22e25 C) in the incubation solution, which contained (in mM): 140 NaCl, 3.5 KCl, 2 CaCl 2 , 1.5 MgCl 2 , 10 glucose, 10 HEPES, pH 7.4, bubbled with 100% O 2 .
For electrical recordings, a reduced SCN preparation was obtained by excising a small piece of tissue (circa one-ninth the size of SCN) from the medial SCN using a fine needle (Cat no. 26002-10, Fine Science Tools, Foster City, CA, USA), followed by further trimming down to 4e10 smaller pieces with a short strip of razor blade. The reduced preparation (containing tens to hundreds of cells, see Fig. 1 of ref. [22]) was then transferred to a coverslip precoated with poly-D-lysine (SigmaeAldrich, St Louis, MO, USA) in a recording chamber for recording. The SCN neurons of the reduced preparation could be identified visually with an inverted microscope (Olympus IX70, Japan). The preparation thus obtained allows rapid application of drugs [23] and has been used to demonstrate diurnal rhythms in both spontaneous firing and Na þ /K þ -ATPase activity [24].

Electrical recordings
Electrical recordings were carried out as described previously [25]. The reduced SCN preparation was perfused with bath

At a glance of commentary
Scientific background on the subject Intercellular coupling is essential for the SCN to serve as a coherent central clock. Whereas synaptic release of neurotransmitters/neuropeptides is critical for synchronizing SCN neurons, non-synaptic communication is also present. In particular, the SCN is tightly packed with small neurons and has abundant perikaryal appositions with narrow extracellular space.

What this study adds to the field
The rat SCN neurons can fire spontaneous action potentials with peak AHP more negative than calculated E K . The result indicates a lower-than-bulk local [K þ ]o sensed by the AHP K þ channels in the K þ diffusion-restricted extracellular space, which may allow for K þ -mediated ionic interactions among neurons to regulate SCN excitability.
solution containing (in mM): 140 NaCl, 3.5 KCl, 2 CaCl 2 , 1.5 MgCl 2 , 10 glucose, 10 HEPES, pH adjusted to 7.4 with NaOH. The perfusion rate was set at 0.6 ml/min and solution change was completed in~1 s judging from the measurement of junction potential. The patch solution contained (in mM): 20 NaCl (high-Na þ ) or 20 KCl (low-Na þ ), 1 CaCl 2 , 2 MgCl 2 , 110 Kgluconate, 11 EGTA, 10 HEPES, 3 Na-ATP, 0.3 Na-GTP, pH adjusted to 7.3 with KOH. The measured liquid junction potential was À12 mV [26] and was corrected for in the presentation of data obtained with whole-cell and perforated-patch recordings. Pipette resistance was 4e6 MU. For perforatedpatch recordings, the patch pipette also included nystatin (SigmaeAldrich, St Louis, MO, USA) at a final concentration of 250 mg/ml prepared from a stock solution (25 mg/ml DMSO). All recordings were made with Axopatch 200B amplifier (Axon Instruments, Foster City, CA, USA) at room temperature (22e25 C). Membrane potentials were recorded using the whole-cell and perforated-patch recording techniques. The signal was low-pass filtered at 1e5 KHz and digitized on-line at 2e10 KHz via a 12-bit A/D digitizing board (DT2821F-DI, Data Translation, Marboro, MA, USA) with a custom-made program written in the C Language. Data were analyzed and plotted with custom-made programs written in Visual Basic 6.0 and the commercial softwares GraphPad PRISM (GraphPad Software, San Diego, CA, USA) and Stata (StataCorp LLC, College Station, Texas, USA). Data are given as means ± SEM and were analyzed with Student's t-test and paired t-test. Two-sample KolmogoroveSmirnov test for equality of distribution functions was used to compare the data distributions between cells recorded with high-Na þ and low-Na þ pipette solutions [ Fig. 3].

Drugs
The stock solution of TTX (0.3 mM in acetic acid) was stored at À20 C and was diluted 1000 times to reach desired final concentrations. TTX was from Tocris Cookson Inc. (Ellisville, MO, USA). Carbachol, Cd 2þ , Ba 2þ and TEA were purchased from SigmaeAldrich.

SCN neurons generate APs with peak AHP negative to calculated E K
The spontaneous firing of rat SCN neurons was investigated using the whole-cell recording technique, with pipette filled with high-Na þ (26 mM Na þ /110 mM K þ ) or low-Na þ (6 mM Na þ /130 mM K þ ) solution. For the experiments, the SCN neurons were recorded in the current-clamp mode after breaking into the whole-cell configuration, and the membrane potential was recorded in 6-s epochs. Only cells with the peak-to-  peak amplitude of the AP larger than 100 mV were included in the analysis. Fig. 1 shows the results from two representative cells in the first minute after breaking into the cells with high-Na þ pipette solution. Fig. 1A shows an epoch of 6 s membrane voltage recorded from a cell firing spontaneous APs with expected magnitudes of peak AP and AHP that were bounded between the calculated values of Na þ equilibrium potential (E Na ) and E K . Fig. 1B shows another cell that fired spontaneous APs with large amplitudes of peak AP and peak AHP beyond calculated E Na and E K , respectively. Comparison of the APs reveals that the faster firing neuron had a faster depolarizing rate of interspike potential, apparently as a result of much larger peak AHP [ Fig. 1C]. Incidentally, the AP threshold (marked by arrows) is also lower for the faster firing neuron (red) than the slower one (blue) [Fig. 1D]. For a total of 72 cells with high-Na þ pipette solution, 27 cells (37%) have peak AP positive to calculated E Na (þ43 mV), 49 cells (68%) peak AHP negative to calculated E K (e88 mV), and 18 (24%) cells both peak AP and peak AHP more positive and negative than calculated E Na and E K , respectively (see Fig. 3A and C; filled bars). In contrast, the resting membrane potential (RMP) was never (0 out of 53 cells) negative to calculated E K (see Fig. 3E, filled bars).
The occurrence of peak AHP negative to calculated E K indicates that local [K þ ] o sensed by the TEA-sensitive AHP K þ channels [see Fig. 7D] must be lower than bulk [K þ ] o , which is clamped by the perfusion bath solution, most likely due to K þ depletion in the narrow ECS facing the membrane by the action of Na þ /K þ -ATPase (NKA). Likewise, the occurrence of peak AP positive to calculated E Na indicates that submembrane local [Na þ ] i sensed by the TTX-sensitive Na þ channels [see Fig. 7A] must be lower than the bulk [Na þ ] i , which is clamped by the high-Na þ pipette solution, most likely also due to extrusion of Na þ via NKA. Because NKA is activated by intracellular Na þ in the rat SCN neurons [27], the large peak AHP negative to calculated E K and peak AP positive to calculated E Na is arguably a consequence of Fig. 3 Distribution and averaged amplitude of peak AP, peak AHP, and RMP between cells recorded with high-Na þ (filled bars) and low-Na þ (open bars) pipette solution. Note the similar distribution of peak AP (10 mV bin size; A), peak AHP (10 mV bin size; C), and RMP (5 mV bin size; E) between the two groups. There is also no difference between high-Na þ and low-Na þ in the average amplitude of peak AP (B), peak AHP (D), and RMP (F). heightened NKA pumping activity due to the use of high-Na þ pipette solution.
Therefore we also used low-Na þ pipette solution to investigate the spontaneous firing. Fig. 2 shows the result obtained from two representative cells, one with peak AP and peak AHP bounded between calculated E Na and E K [ Fig. 2A] and the other with peak AHP negative to calculated E K [ Fig. 2B]. Comparison of the APs again indicates that the faster firing neuron had a faster depolarizing rate of interspike potential, as a result of larger AHP [ Fig. 2C]. Interestingly, the AP threshold (marked by arrows) is actually higher for the faster firing neuron (red) than the slower one (blue) [Fig. 2D]. For a total of 47 cells with low-Na þ pipette solution, none (0%) have peak AP positive to calculated E Na (þ81 mV), but 24 cells (51%) have peak AHP negative to calculated E K (e92 mV) (see Fig. 3A, C; open bars). Again, the RMP was never (0 out of 47 cells) negative to calculated E K (see Fig. 3E, open bars).
Taken together, the results indicate that the SCN neurons could fire APs with peak AHP more negative than calculated E K irrespective of high-or low-Na þ pipette solution, and with peak AP more positive than calculated E Na only using high-Na þ solution. In contrast, RMP was always less negative than calculated E K . Fig. 3 Fig. 3E] between the two groups of cells. There is also no difference between high-Na þ and low-Na þ in the average amplitude of peak AP (33. Fig. 3F]. It is interesting to note that despite the large difference in the values of calculated E Na between high-Na þ (E Na ¼ þ81 mV) and low-Na þ (E Na ¼ þ43 mV) pipette solution, both the distribution  Peak AHP negative to calculated E K may arise later spontaneously The results presented so far were all obtained from the first minute of whole-cell recording. During the course of recording, however, a number of cells were observed to have their peak AHP spontaneously increased to become negative to calculated E K [ Fig. 4]. Fig. 4A shows a representative experiment to demonstrate a cell firing spontaneous APs with peak AP and peak AHP bounded between calculated E Na (þ43 mV) and E K (e88 mV) at the beginning (t ¼ 0) of whole-cell current-clamp recording with high-Na þ electrode solution (leftmost panel). The peak-to-peak amplitude became larger and larger as time passed, with peak AP/AHP increasing/ decreasing from~þ30/e80 mV (t ¼ 0; leftmost panel), to~þ45/ e125 mV (t ¼ 6 min; middle panel), and to~þ70/ e185 mV (t ¼ 14 min; rightmost panel). For this particular cell, the peak AP became positive to calculated E Na and peak AHP negative to calculated E K at t ¼ 6 min (middle panel) and both the peak AP and peak AHP became even larger at t ¼ 14 min (rightmost panel). In sharp contrast, the approximate RMP remained virtually unchanged at e61 mV (marked by arrows).
Parallel to an increase in the magnitude of peak AHP, the firing rate also increased from 5.8 Hz (t ¼ 0; left panel), to 7.2 Hz (t ¼ 6 min; middle panel), and to 11.8 Hz (t ¼ 14 min; right panel) [Fig. 4A], suggesting a correlation of peak AHP with the firing rate. This can be seen by superimposing a selected stretch of recordings with regular firing of a few APs to allow for better comparison of peak AHP with interspike interval as shown in Fig. 4B. The result indicates that the interspike interval decreases, or the firing rate increases, with larger peak AHP. Fig. 4C further expands the region enclosed by the broken lined box [ Fig. 4B] to better illustrate the relation between peak AHP and interspike potential. The earlier increase in the firing rate, from t ¼ 0 (black trace) to t ¼ 6 min (red trace), is correlated with the increase in the slope (depolarizing rate) of interspike potential (marked by arrows) due to the larger peak AHP (red trace). The later increase in the firing rate, from time ¼ 6 (red trace) to t ¼ 14 min (blue trace), is apparently due to a larger depolarization (marked by arrowhead) rebound from a much larger peak AHP (blue trace). The result suggests that a larger peak AHP removes more resting inactivation of inward currents contributing to the interspike potential. For a total of 7 cells having their peak AHP increased spontaneously to become negative to calculated E K , the peak AHP amplitude changed from À82.3 ± 2.2 mV (n ¼ 7) at t ¼ 0 to À126.1 ± 12.4 mV (n ¼ 7; p < 0.05; paired t-test) at t ¼ 3e14 min and the spontaneous firing rate from 2.7 ± 0.9 Hz (n ¼ 7) to 5.6 ± 1.6 Hz (n ¼ 7; p < 0.05; paired t-test). Fig. 5A shows a cell firing spontaneous APs with the peakto-peak amplitude rapidly increased from a value of~160 mV at the beginning of whole-cell recordings to a surprisingly large value of~290 mV in less than 2 min; at the same time RMP gradually depolarized from e91 mV to e74 mV. Unlike the more gradually depolarizing RMP and larger peak AP and AHP, the firing rate increased from 0.5 Hz to 10 Hz more abruptly at a later time. Note that, for this particular cell, on first breaking into the whole-cell recording mode (t ¼ 0), RMP was close to the calculated E K ¼ e92 mV and the AP appeared to be driven by synaptic inputs (leftmost panel, Fig. 5B). Fig. 5C shows the enlarged and expanded voltage trace to illustrate a barrage of depolarizing synaptic potentials (marked by arrows) leading to APs. The cell began to fire spontaneous APs at a rate of 10 Hz when the approximate RMP had reached e74 mV (rightmost panel, Fig. 5B). For comparison, three selected stretch of recordings each from the three 6-s epoch (Fig. 5B, marked by arrowheads) are superimposed in Fig. 5D. The arrows mark the synaptic potentials from the voltage trace recorded at t ¼ 0 (black trace). Fig. 5E expands the region enclosed by the dotted box [ Fig. 5B] to compare the AP driven by synaptic inputs (black and red trace; marked by arrows) with that generated spontaneously (blue trace). The ability to fire spontaneous AP is apparently aided by the unusually large peak AHP (~e220 mV), in spite of relatively negative approximate RMP of e74 mV (dotted line), which allow for more depolarizing interspike potentials (marked by arrowheads) leading to APs.
Peak AHP negative to calculated E K may arise by membrane hyperpolarization We have also encountered cells that increased peak AHP amplitude to become negative to calculated E K in response to hyperpolarizing stimuli [ Fig. 6]. We previously showed that carbachol, a nonspecific cholinergic agonist, mostly inhibits the SCN neurons by acting on muscarinic receptors to open at least background K þ channels, thereby hyperpolarizing RMP and suppressing spontaneous firing [28]. Fig. 6A shows the effect of 100 mM carbachol on the spontaneous firing in a representative SCN neuron. For this particular cell, cholinergic hyperpolarization markedly inhibited spontaneous firing and increased the peak-to-peak amplitude of the remaining APs to have peak AHP become negative to calculated E K . Fig. 6B compares the selected APs (marked by arrowheads, Fig. 6A) in control (black trace) and in carbachol (blue trace). For a total of 6 cells having their peak AHP increased by carbachol to become negative to calculated E K , the peak AHP amplitude changed from À82.8 ± 2.2 mV (n ¼ 6) to À103.5 ± 5.9 mV (n ¼ 6; p < 0.01; paired t-test) and the spontaneous firing rate from 4.5 ± 1.4 Hz (n ¼ 6) to 0.3 ± 0.1 Hz (n ¼ 6; p < 0.05; paired t-test). Fig. 6C shows the first 6 min of voltage recordings from a cell after breaking into the whole cell condition. Negative current injection was applied shortly due to the gradual decrease in the peak-to-peak amplitude of APs, to even smaller than 80 mV, a condition signifying relatively depolarized, fluctuated RMP due to unhealthy or bad recording condition. As indicated, negative current injection reduced the rate of spontaneous firing and increased the amplitude of APs to the point that the peak AP became positive to calculated E Na and the peak AHP negative to calculated E K . Termination of negative current injection rapidly depolarized the RMP and the APs became smaller again with fluctuated peak-to-peak amplitude. Fig. 6D compares the selected APs (marked by arrowheads, Fig. 6C) in the absence (black traces) and presence (blue trace) of negative current injection. Taken together, the rapid, reversible increase in peak AHP to become negative to calculated E K suggests that local [K þ ] o sensed by the AHP K þ channels is already lower than bulk [K þ ] o but the AHP K þ conductance only become large (during hyperpolarizing stimuli) enough to generate peak AHP more negative than calculated E K .
Ionic mechanisms for the peak AHP negative to calculated E K Various channel blockers were used to determine the ionic mechanisms for APs with peak AHP negative to calculated E K , or even with peak AP positive to E Na with high-Na þ pipette solution [ Fig. 7]. Fig. 7A shows the effect of TTX on the spontaneous firing from cells recorded with high-Na þ (left two panels) and low-Na þ (right two panels) pipette solution. As expected, TTX at a concentration of 0.3 mM completely suppress the generation of APs in most cells (right three panels), leaving one cell firing Ca 2þ spikes with much reduced peak AP and negligible AHP (leftmost panel). The results indicate that the TTX-sensitive Na þ channels are responsible for the peak AP positive to calculated E Na when recorded with high-Na þ pipette solution. Fig. 7BeD show the effects of 20 mM Cd 2þ , 3 mM Ba 2þ , and 10 mM TEA on the APs, respectively, recorded from three b i o m e d i c a l j o u r n a l 4 6 ( 2 0 2 3 ) 1 0 0 5 5 1 representative cells. Although the peak AHP amplitude was reduced by Cd 2þ and Ba 2þ , respectively, from À101 ± 2.1 mV (n ¼ 4) to À97 ± 1.7 mV (n ¼ 4; p < 0.01; paired t-test) and from À103 ± 5.4 mV (n ¼ 4) to À99.5 ± 5.6 mV (n ¼ 4; p < 0.05; paired ttest), it remained more negative than calculated E K . As 20 mM Cd 2þ blocks most of the high-voltage-activated Ca 2þ channels [29], and thus Ca 2þ -dependent K þ channels, and 3 mM Ba 2þ blocks large-conductance Ca 2þ -dependent K þ channels (for review, see Ref. [30]), the results suggest a small contribution at best to the observed peak AHP negative to calculated E K . In contrast, 10 mM TEA markedly reduced the peak AHP amplitude [ Fig. 7D1]. Fig. 7D2 shows an epoch of 6 s membrane voltages to indicate the time course of change in the peak AHP in response to the application of 10 mM TEA. Fig. 7D3 compares the selected APs (marked by arrows, Fig. 7D2) in control (black trace) and in the presence of 10 mM TEA (grey, blue, and red trace). As indicated, in~1 s into 10 mM TEA, the peak AHP (blue trace) has become positive to calculated E K . On average, the peak AHP amplitude was reduced by 10 mM TEA from À110.5 ± 5.3 mV (n ¼ 8) to À72.5 ± 4.3 mV (n ¼ 8; p < 0.01; paired t-test). Fig. 7E shows a different set of experiments to determine the dose-dependent effect of TEA on the AP. The result indicates that TEA at submillimolar concentrations effectively reduces the amplitude of peak AHP to become positive to calculated E K . The averaged peak AHP amplitude in control and in 0.3, 1, 3, and 10 mM TEA were, respectively, À96.2 ± 6.2 mV (n ¼ 5), À73.6 ± 3.4 mV (n ¼ 5), À66.4 ± 2.9 mV (n ¼ 5), À60 ± 3 mV (n ¼ 4), and À54 ± 2.3 mV (n ¼ 4).

Peak AHP negative to calculated E K may also occur in perforated-patch recordings
Although much less frequent than with whole-cell recordings, peak AHP negative to calculated E K could also be observed in cells with perforated-patch recordings [ Fig. 8]. For a total of 194 cells, all with high-Na þ pipette solution, 18 cells (9%) have peak AHP negative to calculated E K (e88 mV), and none (0%) have peak AP positive to calculated E Na (þ43 mV). Fig. 8A shows the first minute of membrane voltage recorded from one such cell. Fig. 8B shows a selected stretch of recordings from Fig. 8A to indicate the presence of both fast AHP (marked by arrow) and slow AHP (marked by arrowhead) in perforated-patch APs. Note that only the peak amplitude of fast AHP, but not slow AHP, could become negative to calculated E K . Compared to the whole-cell APs in cells recorded with also high-Na þ pipette solution, two features could be readily distinguished. First, the peak AP amplitude is always small for perforated-patch APs, close to 0 mV at best, irrespective of the peak AHP amplitude. The much smaller peak AP amplitude is most likely due to the high access resistance of perforated-patch recording configuration created by the use of pore-forming nystatin, which would preferentially reduce the amplitude of fast changing voltage as in the upstroke of APs. Second, as indicated in Fig. 8B, the perforated-patch AP has slow AHP (marked by arrowhead) in addition to fast AHP (marked by arrow) (see also Fig. 8D). To better illustrate this point, we compare the APs obtained with perforated-patch and whole-cell recordings [ Fig. 8C and D]. Fair comparison is ensured by selecting the whole-cell voltage having similar RMP and peak AHP to match with the perforated-patch voltage as shown in Fig. 8C. The 6-s epoch of whole-cell voltage (right panel) is from the same cell shown in Fig. 4 at~5 min after breaking into the whole-cell configuration. Note that the whole-cell APs (right panel; 4.7 Hz) have much larger peak AP amplitude albeit with similar RMP and peak AHP as the perforated-patch APs (left panel; 2.2 Hz). Fig. 8D superimposes the selected APs (marked by arrowheads, Fig. 8C) recorded with whole-cell (red trace) and perforatedpatch (blue trace) configuration, indicating that the presence of slow AHP (marked by arrowheads) delays the depolarization of the interspike potential and likely contributes to the lower firing rate in perforated-patch recordings.
In some experiments when nystatin-mediated membrane perforation was slow to allow for clear visualization of the changes in the AP waveform, it may provide an opportunity to determine the dependence of recorded voltage on membrane perforation. Fig. 8E shows two 6-s epochs of membrane voltage recorded at t ¼ 0 (left panel) and 150 s (right panel) into stable perforated-patch recordings. Fig. 8F compares the selected APs (marked by arrows, Fig. 8E) recorded at t ¼ 0 (red trace) and at t ¼ 150 s (blue trace). The result indicate that as time passed the peak AP become larger along with the emergence of fast AHP (marked by arrow), whereas the slow voltage change such as RMP and slow AHP (marked by arrowhead) were virtually unaltered. Fig. 8G expands the time course to better visualize the preferential increase in the amplitude of fast changing voltage as membrane perforation improves.

Discussion
The SCN is tightly packed with small neurons and has abundant perikaryal appositions which may allow for non-synaptic communications such as ephaptic and ionic interactions. In particular, the closely apposed cell bodies with morphological specializations in the narrow ECS [16] could slow molecular diffusion to permit ion accumulation or depletion in the diffusion-restricted ECS. In this study, we show that the SCN neurons can fire APs with TEA-sensitive peak AHP amplitude more negative than calculated E K , indicating that local [K þ ] o in the ECS sensed by the TEA-sensitive AHP K þ channels must be lower than bulk [K þ ] o . This may occur if NKA is also present in the membrane regions facing the diffusion-restricted ECS, so as to control local [K þ ] o to exert specific regulation of peak AHP amplitude and thus neuronal excitability.
Action potentials (APs) with peak AHP more negative than calculated E K We show that the rat SCN neurons could fire spontaneous APs with the amplitude of peak AHP more negative than calculated E K irrespective of high-Na þ [ Fig. 1] or low-Na þ [ Fig. 2] pipette solution. The TEA-sensitive peak AHP amplitude more negative than calculated E K could occur only if local [K þ ] o in the ECS sensed by the TEA-sensitive K þ channels is lower than bulk [K þ ] o (3.5 mM in bath solution) or submembrane local [K þ ] i sensed by the TEA-sensitive K þ channels higher than bulk [K þ ] i (110 or 130 mM in pipette solution). Given a recorded value of peak AHP ¼ e110 mV, for example, a simple calculation according to the Nernst equation indicates that local [K þ ] o in the ECS should be lower than 1.5 (1.8) mM with 110 (130) mM K þ pipette solution or submembrane local [K þ ] i higher than 254 mM, the latter of which is not attainable due to osmotic pressure. Thus to achieve a peak AHP of e110 mV, the energized NKA must transport K þ against its electrochemical gradient to maintain local [K þ ] o in the ECS lower than 1.5 (1.8) mM (compared to bulk [K þ ] o of 3.5 mM) to be sensed by the TEA-sensitive AHP K þ channels. In other words, both NKA and TEA-sensitive AHP K þ channels should be localized to the membrane regions facing the K þ diffusionrestricted ECS.
Nevertheless, cells with local [K þ ] o in the ECS lower than bulk [K þ ] o will not guarantee to fire APs with peak AHP amplitude large enough to become negative to calculated E K . This is because the peak AHP amplitude depends on both the driving force and the K þ conductance. As such, cells with lower local [K þ ] o (i.e. larger driving force) but small K þ conductance could not have large enough peak AHP to become negative to calculated E K . This is best illustrated by the observation of hyperpolarization-evoked rapid, reversible increase in peak AHP to become negative to calculated E K [Fig. 6]. The concomitant increase in both peak AP and peak AHP in response to hyperpolarizing stimuli suggests that membrane hyperpolarization removes resting inactivation of TTX-sensitive Na þ channels (and other voltage-dependent inward current) to increase peak AP, which in turn increase K þ conductance and driving force as well to markedly increase the peak AHP to go beyond calculated E K . In this context, it is not entirely impossible that every SCN neurons have the potential to fire APs with peak AHP large enough to go beyond calculated E K .
The TEA-sensitive AHP is most likely mediated by the fast delayed rectifier K þ channels Kv3.2 and Kv3.1b, which are present in most cell bodies in the mouse SCN [31,32]. These channels are activated at more positive voltages and deactivate very rapidly to allow for high-frequency repetitive firing in many central neurons [33,34]. In particular, Kv3.1b proteins are predominantly expressed in the somatodendritic membrane in the mouse brain [35]. In cerebellar granule cells there are nonuniform distributions of Kv3.1b on the somata, with circular bands of labeling near the axon hillock [36], and in cultural hippocampal neuron, the adaptor protein Ankyrin-G targets Kv3.1b to the axon hillock [37]. Ankyrin-G also colocalizes with Kv3.1b and with Na V 1.1 channel at axonal nodes and heminodes [38,39]. Most recently, Ankyrin-R is found to directly interact with Kv3.1b and is both necessary and sufficient for clustering Kv3.1b K þ channels in the soma to regulate excitability of GABAergic interneurons [40]. RT-PCR analysis showed that the rat SCN expresses mRNAs for all three ankyrin isoforms, Ankyrin-R, Ankyrin-B, and Ankyrin-G (Wan and Huang, unpublished observation). Further work is warranted to investigate the somatic colocalization of Kv3.1b with NKA a-isoforms and with Ankyrin-G or Ankyrin-R, in a hope to help localize the presumed K þ diffusion-restricted ECS regions in the rat SCN.
Action potentials (APs) with peak AP more positive than calculated E Na The SCN neurons could also fire spontaneous APs with peak AP more positive than calculated E Na if pipette was filled with high-Na þ solution. The peak AP amplitude more positive than calculated E Na (þ43 mV) could occur only if local [Na þ ] o in the ECS sensed by the TTX-sensitive Na þ channels is higher than bulk [Na þ ] o (140 mM in bath solution) or submembrane local [Na þ ] i sensed by the TTX-sensitive Na þ channels lower than bulk [Na þ ] i (26 mM in pipette solution). Given a recorded value of peak AP ¼ þ60 mV, for example, local [Na þ ] o in the ECS sensed by the TTX-sensitive Na þ channels should be higher than 269 mM or submembrane local [Na þ ] i lower than 16 mM, the former of which is not attainable due to osmotic pressure.
Thus to achieve a peak AP of þ60 mV, the energized NKA must transport Na þ against its electrochemical gradient to maintain submembrane local [Na þ ] i to lower than 16 mM (compared to bulk [Na þ ] i of 26 mM) to be sensed by the TTX-sensitive Na þ channels.
Further support for submembrane local [Na þ ] i being different from bulk [Na þ ] i comes from the observation that cells recorded with high-Na þ (26 mM Na þ ) or low-Na þ (6 mM Na þ ) pipette solution had similar peak AP amplitude despite the marked difference in calculated E Na between high-Na þ (E Na ¼ þ43 mV) and low-Na þ (E Na ¼ þ81 mV) [ Fig. 3A and B]. A simple explanation for this is that both have similar submembrane local [Na þ ] i around the TTX-sensitive Na þ channels, although their bulk [Na þ ] i differ markedly, being 26 mM and 6 mM. To estimate submembrane local [Na þ ] i sensed by the TTX-sensitive Na þ channels, we considered only large peak AP amplitude, for example, between þ55 mV and the largest recorded amplitude of þ67.5 mV, so that the recorded peak AP would be close to and thus a good measure of true E Na . A simple calculation according to the Nernst equation yields 15 mM and 10 mM submembrane local [Na þ ] i , respectively, for peak AP amplitude of þ55 mV and þ67.5 mV, assuming [Na þ ] o ¼ 140 mM clamped by the bath solution. The assumption of [Na þ ] o being clamped at 140 mM by the bath solution is reasonable even if the TTX-sensitive Na þ channels also reside in the K þ diffusionrestricted ECS, because [Na þ ] o is unlikely to increase too much beyond 140 mM due to the constrain imposed by the corresponding increase in the osmotic pressure.
It is interesting to note that the largest peak AP amplitude recorded with either high-Na þ or low-Na þ pipette solution was incidentally the same, with a value of þ67.5 mV. This may set a lower limit concentration of~10 mM submembrane local [Na þ ] i around the TTX-sensitive Na þ channels. No matter what submembrane local [Na þ ] i is, it is a result of combined actions of NKA-mediated Na þ extrusion and Na þ entry via the TTX-sensitive Na þ channels and non-desensitizing Na þ conductances. In this context, it is worth mentioning of our previous findings suggesting that submembrane local [Na þ ] i around the NKA Na þ pump sites is not clamped by the pipette solution [27]. Specifically we demonstrated finite NKA Na þ pumping activity with Na þ -free pipette solution in the presence of TTX, suggesting finite submembrane local [Na þ ] i around the NKA Na þ pump sites, apparently mediated by Na þ entry via TTX-insensitive Na þ routes [27]. Nevertheless, there remains a possibility that the pipette solution may not sufficiently diffuse into the dendrites during the recording period and only partially modifies [Na þ ] i .

Comparison of whole-cell and perforated-patch APs
The SCN neurons could also, but rarely, fire APs with peak AHP more negative than calculated E K with perforated-patch recordings. The rare occurrence of peak AHP negative to calculated E K is most likely due to the less than perfect electrical access between the recording electrode and cytosol for perforated-patch compared to whole-cell recordings. The high access (series) resistance would low-pass filter the measured signal, thereby attenuating particularly the fast changing voltage such as the upstroke of an AP, as suggested by comparing APs recorded with perforated-patch and whole-cell recordings [ Fig. 8C and D]. The preferential attenuation of fast changing voltage with perforated-patch recordings could also be demonstrated by the result of selective increase in both the peak AP and peak AHP as time passes to achieve better membrane perforation by nystatin [Fig. 8EeG]. The same reasoning can also explain the lack of observation of peak AP positive to calculated E Na with high-Na þ pipette solution.
An additional difference is the presence of slow AHP with perforated-patch, but not whole-cell, recordings [ Fig. 8D]. This difference is most likely due to the buffering of cytosolic Ca 2þ by EGTA in the pipette with whole-cell recordings. Indeed, our preliminary result indicated that the slow AHP is mediated by Ca 2þ -dependent K þ current. The presence of slow AHP, as opposed to fast AHP, prolongs the interspike interval and may contribute to the lower spontaneous firing rate recorded with cell-attached and perforated-patch recordings than with whole-cell recordings (unpublished results).

K þ diffusion-restricted extracellular space (ECS) in the rat SCN
The results, peak AHP amplitude more negative than calculated E K , presented in this study indicates that local [K þ ] o in the ECS sensed by the TEA-sensitive K þ channels must be lower than bulk [K þ ] o . To account for this, note that local [K þ ] o in the narrow ECS can be described with a macroscopic diffusion equation that includes terms for diffusion, source (K þ release via K þ channels), and sink (K þ clearance via NKA) [41]. The diffusion of K þ is hindered due to the narrow ECS with intricate structure that effectively slows the diffusion of K þ compared to unrestricted free diffusion in bulk solution. When aided by K þ clearance via NKA in the small volume of ECS, local [K þ ] o around the TEA-sensitive AHP K þ channels could become lower than bulk [K þ ] o .
The suggested presence of K þ diffusion-restricted ECS is not inconsistent with the ECS geometry in the rat SCN. The SCN is tightly packed with small size of neurons, which are among the smallest in the brain, as well as abundant perikaryal appositions [16]. The neuronal cell bodies are closely apposed with or without intervening glial elements, and closely apposed neurons without an intervening glial element may possess electron-dense materials or punctate densities between them. There are also unusual series of punctate junctions, so-called zipper junctions, between cell bodies and sometime between cell body and axon terminals. Interestingly, many mitochondria, along with smooth endoplasmic reticular, are seen close to the zipper junction between cell bodies. Close appositions between neurons and glia can also be revealed by electron microscopic analysis [16]. It is likely that the abundant perikaryal appositions with morphological specializations in the narrow ECS increases the tortuosity to slow the diffusion of K þ , allowing it to be cleared by NKA to maintain a lower local [K þ ] o in the ECS than bulk [K þ ] o .

Functional implications
The brain ECS is composed of fluid-filled spaces laden with extracellular matrix and measurement of ECS tortuosity suggests that the ECS is a highly connected space so that any b i o m e d i c a l j o u r n a l 4 6 ( 2 0 2 3 ) 1 0 0 5 5 1 location in the ECS could be reached by multiple pathways except for some dead-space microdomains [42e44]. In essence, the ECS supplies a reservoir of ions for electrical signalling and mediates chemical signalling through volume transmission [43,44]. Nevertheless, local K þ fluctuation is not considered very useful as a signalling molecule due to its nonspecific effect on membrane potentials [43,44]. Our results suggest that this may not be the case in the rat SCN. We showed that only TEAsensitive fast AHP, but not RMP, could become negative to calculated E K . Furthermore, no change in RMP was observed during the course of spontaneous increase in peak AHP to become negative to calculated E K [Fig. 4]. The results suggest differential localization of K þ channels for AHP and for RMP to different membrane regions facing different local environments. Most likely, both the TEA-sensitive AHP K þ channels and NKA are at membrane regions facing the same K þ diffusionrestricted ECS such that NKA can clear K þ to maintain a lower local [K þ ] o than bulk [K þ ] o . In the case of TEA-sensitive AHP K þ channels, local [K þ ] o may be controlled to specifically regulate the peak AHP. Different combinations of NKA and other K þ channels in other similarly K þ diffusion-restricted ECS may regulate local [K þ ] o to play different, specific roles. In this sense, local K þ fluctuation could be useful as a signalling molecule in K þ diffusion-restricted ECS.
The functional presence of K þ diffusion-restricted ECS, in which local [K þ ] o is balanced by K þ clearance via NKA and K þ release via K þ channels, may allow for K þ -mediated ionic interactions among neurons to regulate SCN physiology. Our results suggest such a possibility at least for the AHP, which plays a role in the regulation of AP firing in the SCN neurons [45e50]. Our results show that, at least with whole-cell recordings, cells having larger peak AHP, particularly when negative to calculated E K , had higher firing rate. In other words, local [K þ ] o in the ECS around and sensed by the TEAsensitive AHP K þ channels plays a role in the regulation of neuronal excitability. Intercellular coupling via ionic interactions among neurons may become possible if the K þ diffusion-restricted ECS is shared locally, or even more broadly, by a number of cells.

Conclusion
The rat SCN neurons can fire APs with TEA-sensitive peak AHP more negative than calculated E K . The result indicates that local [K þ ] o in the ECS around and sensed by the TEA-sensitive K þ channels must be lower than bulk [K þ ] o . Such a lower local [K þ ] o can be achieved by NKA-mediated K þ clearance in K þ diffusion-restricted ECS. Since local [K þ ] o in the K þ diffusionrestricted ECS regulates peak AHP, which plays a role in regulating SCN neuronal firing, the K þ diffusion-restricted ECS may allow for K þ -mediated ionic interactions among neurons to regulate SCN excitability.

Conflicts of interest
None.